You might as well do a twofer if you are going for Shadows Mountain, and hit White Horse Hills too. There's a great description of the area and part of the trail under the White Horse Hills page by Hippiepunkpirate. I started at the trail head to the Arizona Trail off FR 418 and followed the trail north for about 0.5 miles to the saddle. At the saddle there is what some might call a trail to the top of White Horse Hills, but it appears to be an old ATV road. It has a bunch of trees fallen over it. I suppose if you were only going for White Horse Hills, the trail would be a good route to the top.
Continue on the Arizona Trail until you reach the bottom of the drainage on the northeast side of White Horse. You will have to find a good place to cross the ravine. You should pick up a more defined trail there (don't know the name) which will take you around White Horse heading west to the base of Shadows. At this point just before the trail heads down the hill to the west, I started the bushwhacked to the top. It's very steep but there's a lot of vegetation so the footing is good most of the way. It's only about 500 feet elevation gain.
After completing Shadows I followed the route I took in reverse back down to the unnamed trail and over to the ravine, but I veered up the side of white horse about the time I needed to hop off the unnamed trail. Stay on the west side of the drainage and hug the aspen tree line up White Horse. It flattens as you reach the ridgeline on this bushwhack, which you can follow the rest of the way to the top.
Once I finished White Horse, I just made a beeline for the trail in the saddle. I could have followed the trail down, but strait down was faster.
Check out the Official Route and Triplog.
This is a moderately difficult hike.